Dear Jimmy,
This mild elevation may represent a decrease blood level of your medication. You should inform your physician and let them know and they may want to provide you with a longer acting medication.
Mild elevations of BP over a long time may increase the likliehood of LVH.
Blood Pressure is supposed to be the lowest while in Bed sleeping and may rise and peak not too long after waking up but before Breakfast.
It should fluctuate but usually not too much higher than that peak level in the morning. Arguments, stress, eating and others can affect it. As I'm sure you know, the best target to shoot for is 120/80.
Another factor I wanted to mention is that one should wait at least 5-10 minutes between readings or more. Several subsequent measurements can alter it also, and I wonder if that's not what's happening with your tests at 5 AM. I'm assuming 5AM is when you get up to get ready for work or something. If that's the case, then it would make sense that this is when it should peak and lower in the next few hours, and then fluctuate mildly throughout the day.
But then you mention going back to sleep? Why are you getting up at 5am to check it and then go back to sleep?
Maybe others can enlighten us as to whether you're causing yourself worry about it, therefore waking up worrying about it (elevating it) and then by taking "too many" measurements too close together it may even read even worse?
And 125/85 is an excellent target.
I wouldn't worry but talk to your doctor about your concerns also.
Thank you for your comments.